Optimal. Leaf size=49 \[ -\frac{250 x}{81}+\frac{185}{81 (3 x+2)}-\frac{107}{486 (3 x+2)^2}+\frac{7}{729 (3 x+2)^3}+\frac{1025}{243} \log (3 x+2) \]
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Rubi [A] time = 0.0200679, antiderivative size = 49, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05, Rules used = {77} \[ -\frac{250 x}{81}+\frac{185}{81 (3 x+2)}-\frac{107}{486 (3 x+2)^2}+\frac{7}{729 (3 x+2)^3}+\frac{1025}{243} \log (3 x+2) \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int \frac{(1-2 x) (3+5 x)^3}{(2+3 x)^4} \, dx &=\int \left (-\frac{250}{81}-\frac{7}{81 (2+3 x)^4}+\frac{107}{81 (2+3 x)^3}-\frac{185}{27 (2+3 x)^2}+\frac{1025}{81 (2+3 x)}\right ) \, dx\\ &=-\frac{250 x}{81}+\frac{7}{729 (2+3 x)^3}-\frac{107}{486 (2+3 x)^2}+\frac{185}{81 (2+3 x)}+\frac{1025}{243} \log (2+3 x)\\ \end{align*}
Mathematica [A] time = 0.0174507, size = 47, normalized size = 0.96 \[ \frac{-1500 (3 x+2)+\frac{3330}{3 x+2}-\frac{321}{(3 x+2)^2}+\frac{14}{(3 x+2)^3}+6150 \log (3 x+2)}{1458} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 40, normalized size = 0.8 \begin{align*} -{\frac{250\,x}{81}}+{\frac{7}{729\, \left ( 2+3\,x \right ) ^{3}}}-{\frac{107}{486\, \left ( 2+3\,x \right ) ^{2}}}+{\frac{185}{162+243\,x}}+{\frac{1025\,\ln \left ( 2+3\,x \right ) }{243}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.07782, size = 55, normalized size = 1.12 \begin{align*} -\frac{250}{81} \, x + \frac{29970 \, x^{2} + 38997 \, x + 12692}{1458 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )}} + \frac{1025}{243} \, \log \left (3 \, x + 2\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.69692, size = 193, normalized size = 3.94 \begin{align*} -\frac{121500 \, x^{4} + 243000 \, x^{3} + 132030 \, x^{2} - 6150 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )} \log \left (3 \, x + 2\right ) - 2997 \, x - 12692}{1458 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.131947, size = 39, normalized size = 0.8 \begin{align*} - \frac{250 x}{81} + \frac{29970 x^{2} + 38997 x + 12692}{39366 x^{3} + 78732 x^{2} + 52488 x + 11664} + \frac{1025 \log{\left (3 x + 2 \right )}}{243} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.8577, size = 43, normalized size = 0.88 \begin{align*} -\frac{250}{81} \, x + \frac{29970 \, x^{2} + 38997 \, x + 12692}{1458 \,{\left (3 \, x + 2\right )}^{3}} + \frac{1025}{243} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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